Summarize:

Be sure to support your child's head and neck while you do this. You might have more success lifting your baby higher, so that his or her belly is resting on your shoulder. You might want to put a burping cloth over your shoulder, especially if the child is under a year old. The bottom of their esophagus (the tube that brings food into the stomach) is not all the way developed and may be briefly sent out of whack when the baby burps. This sometimes causes them to spit up, but is perfectly natural. Do this very gently.  You should only pat them using wrist action; do not move your arm in order to burp your baby. If you don't want to pat your baby, you can also rub his or her back using a circular motion with your hand. Although a bit less effective, it often accomplishes the same thing. It might sound like a normal burp, and if it does, you know to stop. Otherwise, it could sound like a sneeze, a grunt, or just a brief, "Ump." Establish your presence again and give your baby a kiss.
Hold the baby over your shoulder. Pat them between the shoulder blades. Know when the baby burped, and stop patting. Put them in front of you as soon as they burp, and show them your smiling face.